Grilling is a little extra work in this recipe but will add great flavor to all components of the dish. If you’re going to be short on time or just prefer to cook indoors, skip the skewers altogether - everything will come together quickly on the stovetop.
If cooking on the grill: Heat a grill to 400F / 204C, keeping one part over direct heat and one part over indirect heat.
{grill}: Brush some cooking oil onto grates and onto avocados (cut-side only) and corn.
{grill}: Place corn over direct heat and rotate to get grill marks on all sides. Move to indirect heat and continue cooking with the lid closed until tender, 4 to 6 minutes.
{grill}: When corn is nearly tender, place avocado halves, cut-side down, over direct heat. Add shrimp skewers to direct heat and cook on both sides until opaque. Avocado halves should have grill marks about the same time that shrimp is cooked through, 4 to 6 minutes for both.
If cooking on the stovetop: Bring a large stock pot of salted water to a boil.
{stovetop}: When water is boiling, add corn and boil until tender, 5 to 7 minutes.
{stovetop}: Heat a wok or skillet with some cooking oil over medium heat. Add shrimp and saute until opaque and cooked through, 3 to 5 minutes.
Transfer shrimp to a cutting board (discard skewers if you cooked on the grill). Add cilantro and chop shrimp and cilantro into small pieces.
Combine shrimp, cilantro, and cheese.
Heat a large nonstick pan over medium heat. Place a tortilla in the pan, top it with shrimp / cheese mixture and then another tortilla.
When the tortilla on the bottom is golden brown and crisp, flip the quesadilla and cook on the other side until all of the cheese is melted. Continue with the remaining tortillas and filling.
Scoop out avocado and mash with first part of lime juice. Season with some salt and pepper.
Brush corn with butter and second part of lime juice. Sprinkle chili powder over top.
Slice quesadillas into wedges. Serve with sour cream and mashed avocado. Enjoy with corn on the side.